Transducer Apparatus as well as Measuring System formed therewith

ABSTRACT

A transducer apparatus comprises a transducer housing, a tube as well as a temperature sensor. The tube is arranged within a cavity of the transducer housing, in such a manner that an intermediate space is formed between a wall of the transducer housing facing the cavity inner surface and an outer surface of a wall of the tube facing the cavity. The tube is adapted to guide a fluid in its lumen, in such a manner that an inner surface of the wall of the tube facing the lumen is contacted by fluid guided in the lumen. The temperature sensor is formed by means of two temperature detectors arranged within the intermediate space as well as by means of a coupling body coupling the temperature detector thermally conductively with the wall of the tube as well as by means of a coupling body coupling the temperature detector thermally conductively with the temperature detector and is additionally adapted to register a particular measurement location temperature, namely a temperature at a first, respectively second, temperature measurement location formed by means of the respective temperature detector, and to transduce such into a corresponding temperature measurement signal, namely an electrical measurement signal representing the particular measurement location temperature.

The invention relates to a transducer apparatus suitable for measuring a target temperature of the transducer apparatus, equally as well, a time variable target temperature, especially a temperature of a fluid guided in a lumen of a tube, and/or a temperature of a wall of such a tube contacted by the fluid. Furthermore, the invention relates also to a measuring system formed by means of such a transducer apparatus.

Transducer apparatuses of the type being discussed comprise a transducer housing having a cavity encased by a wall, typically a metal wall, as well as a tube having a lumen surrounded by a wall, typically likewise a metal wall, and arranged within the cavity of the transducer housing, in such a manner that, between an inner surface of the wall of the transducer housing facing the cavity and an outer surface of the wall of the tube, namely an outer surface of the wall of the tube facing the cavity, an intermediate space is formed, most often an intermediate space filled with air or an inert gas. The at least one tube is, especially, adapted to guide in its lumen a fluid flowing, at least at times, for example, a fluid in the form of a gas, a liquid or a flowable dispersion, in such a manner that an inner surface of the wall of the tube facing the lumen is contacted by fluid guided in the lumen to form a first interface of first type, namely an interface between a fluid and a solid phase.

In order to measure a target temperature, namely a temperature of the respective transducer apparatus, equally as well a time variable temperature, at a predefined measuring, respectively reference, point within the respective transducer apparatus, such transducer apparatuses comprise, furthermore, most often, two or more temperature sensors formed, in each case, by means of a temperature detector arranged within the intermediate space and, consequently, during operation not contacted by the fluid in the lumen of the at least one tube, wherein at least one of the temperature sensors has a coupling body connecting its temperature detector thermally conductively with the wall, for example, a coupling body formed by means of thermally conductive adhesive. Each of such temperature detectors can be, for example, a platinum measuring resistor, a thermistor or a thermocouple or, however, electrical circuits formed by means of a plurality of such temperature sensitive, electrical, respectively electronic, components. Each of the temperature sensors is adapted to transduce a measurement location temperature corresponding to a temperature at a temperature measurement location formed by means of the respective temperature detector, in each case, into a corresponding temperature measurement signal, namely an electrical measurement signal representing the particular measurement location temperature, for example, an electrical measurement signal having an electrical signal voltage dependent on the measurement location temperature and/or an electrical signal current dependent on the measurement location temperature. Target temperature in the case of such transducer apparatuses can be, for example, a measured fluid temperature, namely a temperature of the fluid guided during operation of the transducer apparatus in the lumen of the at least one tube, and/or a tube temperature, namely a temperature of the wall of the tube contacted by the fluid respectively located in the lumen.

The transducer apparatus can, furthermore, be connected to a measuring and operating electronics, formed, for example, by means of at least one microprocessor, to form a measuring system for measuring at least one measured variable, for example, namely the temperature of the measured fluid or also a density and/or a viscosity of the fluid guided in the at least one tube of the respective transducer apparatus. The measuring and operating electronics can, in turn, be adapted, with application of the at least two temperature measurement signals generated by means of the transducer apparatus, to generate a measured value, which represents the at least one measured variable. In the case of such measuring systems, the measuring and operating electronics is typically accommodated within at least one, comparatively robust, especially impact-, pressure-, and/or weather resistant, electronics housing. The electronics housing can, for example, be arranged removed from the transducer system and connected with such only via a flexible cable; it can, however, also be directly arranged on the transducer housing, respectively affixed thereto. Further examples of transducer apparatuses of the type being discussed, respectively measuring systems formed therewith, are shown in, among others, EP-A 919 793, US-A 2004/0187599, US-A 2008/0127745, US-A 2011/0113896, U.S. Pat. No. 4,768,384, U.S. Pat. No. 5,602,346, U.S. Pat. No. 6,047,457, U.S. Pat. No. 7,040,179, U.S. Pat. No. 7,549,319, WO-A 01/02816, WO-A 2009/051588, WO-A 2009/134268, WO-A 2012/018323, WO-A 2012/033504, WO-A 2012/067608 or WO-A 2012/115639.

In the case of measuring systems of the above indicated type used in industrial measuring and automation technology, the particular measuring and operating electronics is usually electrically connected via corresponding electrical lines also to a superordinated electronic data processing system arranged most often spatially removed from the respective measuring system and most often also spatially distributed, to which the measured values produced by the respective measuring system and correspondingly carried by means of at least one of these measured value signals are forwarded near in time, for example, also in real time. Measuring systems of the type being discussed are additionally usually connected with one another and/or to corresponding electronic process controllers by means of a data transmission network provided within the superordinated data processing system, for example, to programmable logic controllers (PLC) installed on-site or to process control computers installed in a remote control room, where the measured values produced by means of the respective measuring system and digitized in suitable manner and correspondingly encoded are forwarded. By means of such process control computers, the transmitted measured values can be further processed and visualized as corresponding measurement results e.g. on monitors and/or converted into control signals for other field devices, such as e.g. magnet-operated valves, electric motors, etc., embodied as actuating devices. Since modern measuring arrangements can also be monitored and, in given cases, controlled and/or configured most often directly from such control computers, in corresponding manner, operating data intended for the measuring system are equally sent via the aforementioned data transmission networks, which are most often hybrid as regards the transmission physics and/or the transmission logic. Accordingly, the data processing system usually also serves to condition, for example, suitably to digitize and, in given cases, to convert into a corresponding telegram, the measured value signal delivered by the measuring system, corresponding to the requirements of downstream data transmission networks, and/or to evaluate such on-site. For such purpose, there are provided in such data processing systems, electrically coupled with the respective connecting lines, evaluating circuits, which pre- and/or further process as well as, in case required, suitably convert the measured values received by the respective measuring system. Serving for data transmission in such industrial data processing systems at least sectionally, especially serially, are fieldbusses, such as e.g. FOUNDATION FIELDBUS, RACKBUS-RS 485, PROFIBUS, etc., fieldbusses, or, for example, also networks based on the ETHERNET standards, together with the corresponding, most often comprehensively standardized, transmission protocols. Alternatively or supplementally, in the case of modern measuring systems of the type being discussed, measured values can also be transmitted wirelessly per radio to the particular data processing system. Besides the evaluating circuits required for processing and converting the measured values delivered from the respectively connected measuring systems, such superordinated data processing systems have most often also electrical supply circuits serving for supplying the connected measuring systems with electrical energy and providing a corresponding supply voltage, in given cases, fed directly by the connected fieldbus, for the respective electronics and the thereto connected electrical lines and driving electrical currents flowing through the respective electronics. A supply circuit can, in such case, be associated with, for example, exactly one measuring system, respectively a corresponding electronics, and be accommodated together with the evaluating circuit associated with the respective measuring system, for example, combined in a corresponding fieldbus adapter, in a shared electronics housing, e.g. formed as a top hat rail module. It is, however, also quite usual to accommodate supply circuits and evaluating circuits in separate electronics housings, in given cases, spatially remotely from one another, and to connect them correspondingly together via external cables.

Transducer apparatuses of the type being discussed are applied not least of all also in vibronic measuring systems serving for ascertaining measured variables, for example, a mass flow rate, a density or a viscosity, of fluids guided in a process line, for example, a pipeline, respectively they can be an integral component of such a measuring system. Construction and operation of such vibronic measuring systems formed by means of such a transducer apparatus, for example, also measuring systems in the form of Coriolis, mass flow, measuring devices or also Coriolis, mass flow, measuring systems, are known, per se, to those skilled in the art and are described at length and in detail, for example, also in the above mentioned EP-A 919 793, US-A 2004/0187599, US-A 2008/0127745, US-A 2011/0113896, U.S. Pat. No. 4,768,384, U.S. Pat. No. 5,602,346, U.S. Pat. No. 7,040,179, U.S. Pat. No. 7,549,319, WO-A 01/02816, WO-A 2009/051588, WO-A 2009/134268, WO-A 2012/018323, WO-A 2012/033504, WO-A 2012/067608, WO-A 2012/115639, or, for example, also in US-A 2001/0037690, US-A 2011/0265580, US-A 2011/0146416, US-A 2011/0113896, US-A 2010/0242623, WO-A 2013/092104, WO-A 01/29519, WO-A 98/02725, WO-A 94/21999 or WO-A 88/02853. In the case of such vibronic measuring systems, the at least one tube of the respective transducer apparatus is, especially, also adapted, for the purpose of measuring the at least one measured variable, during operation, at least at times, to be caused to vibrate while filled with fluid to be measured, respectively flowed through by the fluid to be measured. Typically, the at least one tube is actively excited by means of at least one electromechanical oscillation exciter of the transducer apparatus acting thereon, for example, an oscillation exciter formed by means of a permanent magnet affixed to the at least one tube and by means of an exciter coil interacting therewith, to execute wanted oscillations, namely mechanical oscillations about a static resting position associated with the respective tube, especially also mechanical oscillations, which are suitable to induce in the flowing fluid Coriolis forces dependent on a mass flow rate, m, and/or which are suitable to induce in the flowing fluid frictional forces dependent on a viscosity, η, and/or which are suitable to induce in the flowing fluid inertial forces dependent on a density, ρ. For registering mechanical oscillations of the at least one tube, not least of all also its wanted oscillations, the transducer apparatuses used in such vibronic measuring systems have, furthermore, in each case, at least one oscillation sensor, for example, an electrodynamic, oscillation sensor, which is adapted to produce at least one oscillatory signal, namely an electrical measurement signal representing oscillatory movements of the at least one tube, for example, with an electrical signal voltage dependent on a velocity of the oscillatory movements of the at least one tube. The measuring and operating electronics of such vibronic measuring systems is—not least of all for the case, in which the at least one measured value represents a density or a viscosity of the fluid guided in the at least one tube —, further adapted to generate the at least one measured value using both the at least two temperature measurement signals generated by means of the transducer apparatus as well as also the at least one oscillation signal, for example, in such a manner that the measuring and operating electronics ascertains the at least one measured value based on a wanted frequency measured based on the oscillation signal, namely an oscillation frequency of the wanted oscillations dependent on the measured variable to be measured and for this purpose metrologically compensates a possible dependence of the wanted frequency also on an instantaneous, measured fluid temperature, respectively a temperature distribution within the wall of the at least one tube.

In the case of modern measuring systems used in industrial measuring and automation technology, not least of all also in the case of vibronic measuring systems of the above indicated type, the measuring and operating electronics is most often formed by means of one or more microprocessors, in given cases, also implemented as digital signal processors (DSP), in such a manner that the measuring and operating electronics ascertains the respective measured values for the at least one measured variable by numerical processing of digital, sampled values of measurement signals of the respective transducer apparatus, for example, namely digital, sampled values won from the at least two temperature measurement signals, respectively the at least one oscillatory signal, and provided in the form of corresponding digital values. Besides the evaluation of the temperature measurement signals as well as the at least one oscillation signal, the measuring and operating electronics of vibronic measuring systems of the above indicated type serves typically also to generate at least one driver signal, for example, a harmonic and/or clocked, driver signal, for the at least one electromechanical oscillation exciter. Said driver signal can be controlled, for example, as regards an electrical current level and/or a voltage level.

As evident, among others, from the above mentioned U.S. Pat. No. 4,768,384, U.S. Pat. No. 7,040,179, respectively US-A 2008/0127745, a special problem of ascertaining a temperature in transducer apparatuses of the type being discussed, be it a measured fluid temperature or a tube temperature, is that the measurement location temperatures registered by means of the two, in given cases, also three or more, temperature sensors correspond, first of all, in each case, actually only to a local temperature at exactly the temperature measurement location formed by means of the respective temperature detector, that, however, conversely, most often actually a local, respectively average temperature at another apparatus reference point, namely a reference point within the transducer apparatus remote from each of the temperature measurement locations, is of interest (target temperature), for example, namely—not least of all for the purpose of ascertaining the measured fluid temperature—a temperature within the lumen of the at least one tube, and/or—not least of all for the purpose of correction of a dependence of the wanted frequency on a spatial temperature distribution within the wall of the at least one tube—actually a spatially averaged tube temperature should serve as a target temperature. A further problem can additionally be that as a result of unavoidable time changes of the measured fluid temperature within the transducer apparatus regularly also dynamic heat equilibration processes can take place, which likewise, not least of all due to the only very limited number of temperature measurement locations, respectively due to their mutual spatial separation, can lead to defective measurement results in measuring systems formed by means of transducer apparatuses of the type being discussed, be it in the case of ascertaining the measured fluid temperature or, for instance, in the case of application of the transducer apparatus in a vibronic measuring system, in the case of which measured variables, such as e.g. the density and/or the viscosity of a fluid guided in the at least one tube or also a mass flow rate of a fluid flowing through the at least one tube, are ascertained based on wanted oscillations of the at least one tube. Moreover, such as also discussed, among others, in the above mentioned WO-A 2009/051588, also an ambient temperature of the transducer, namely a temperature of an atmosphere surrounding the transducer housing, respectively a time change of the ambient temperature, can degrade the accuracy, with which the measured fluid temperature, respectively the tube temperature, can be ascertained by means of such transducer apparatuses.

Further investigations on the part of the inventors have, furthermore, shown that, besides the above indicated influences, surprisingly, also a temperature difference, respectively its time change, existing between the measured fluid temperature and the tube ambient temperature, namely a temperature of the fluid volume in the intermediate space formed between the inner surface of the wall of the transducer housing and the outer surface of the wall of the tube, consequently the fluid volume surrounding the tube, can influence the respective temperature measurement signals. Fundamentally, each of the temperature sensors is thermally coupled, more or less strongly, via a respective surface facing the intermediate space, also to the fluid volume kept in the intermediate space, in such a manner that a heat transfer taking place between the fluid within the lumen of the tube and the fluid volume surrounding the tube regularly leads also partially through the respective temperature sensors. Due to such heat transfer, respectively also due to associated heat transport processes respectively transpiring between each of the temperature sensors and the fluid volume formed in the intermediate space, the respective measurement location temperature is, thus, dependent not only on the tube temperature, respectively the measured fluid temperature, but, instead, regularly also mentionably co-determined by the ambient temperature of the tube. Moreover, the inventors could also detect that this thermal coupling can, at times, assume such an extent that, as regards the high accuracy of measurement desired for measuring systems of the type being discussed, not least of all also for vibronic measuring systems, it is actually no longer negligible, respectively that, conversely, an ignoring of the influence of such temperature difference on the respectively registered measurement location temperature, respectively the temperature measurement signal representing such, can lead to quite significant measurement errors, for instance, in such a manner that the measured values for the target temperature ascertained, in each case, by means of the respective measuring system, especially also in the case of time constant target temperature, deviate, at times, by more than 0.5 K from the actual, respectively true, target temperature.

Taking this into consideration, an object of the invention is so to improve transducer apparatuses of the aforementioned type that even with two temperature sensors arranged, in each case, outside of the lumen of the at least one tube, equally as well within the transducer housing, an (in comparison to conventional transducer apparatuses) more precise ascertaining of a target temperature, for example, namely the measured fluid temperature and/or a tube temperature, reigning at a predetermined, respectively earlier fixed, equally as well removed from each of the at least two temperature sensors, apparatus reference point located within the transducer housing is enabled, respectively that the target temperature, lying not least of all also in a typical working range for transducer apparatuses of the type being discussed, for instance, between −40° C. and +150° C., can be determined with a measuring error of less than 0.2 K; this not least of all also for the case, in which the particular tube temperature, respectively measured fluid temperature and/or the particular transducer—, respectively tube, ambient temperature varies in an unpredictable manner with respect to time, respectively the temperature difference existing between the measured fluid temperature and the tube ambient temperature fluctuates over a broad temperature range.

For achieving the object, the invention resides in a transducer apparatus, which comprises a transducer housing having a cavity encased by a wall, for example, a metal wall, as well as a tube having a lumen surrounded by a wall, for example, a metal wall, wherein the tube is arranged within the cavity of the transducer housing in such a manner that between an inner surface of the wall of the transducer housing facing the cavity and an outer surface of the wall of the tube facing the cavity an intermediate space is formed, and wherein the tube is adapted to guide in its lumen a fluid, especially a fluid flowing at least at times, for example, a gas, a liquid or a flowable dispersion, in such a manner that an inner surface of the wall of the tube facing the lumen is contacted by fluid guided in the lumen in order to form a first interface of first type, namely an interface between a fluid and a solid phase; as well as a temperature sensor formed by means of a first temperature detector arranged within the intermediate space, for example, a first temperature detector formed by means of a platinum measuring resistor, a thermistor or a thermocouple, by means of a first coupling body coupling the first temperature detector thermally conductively with the wall of the tube, by means of a second temperature detector arranged within the intermediate space and spaced from the first temperature detector, for example, a second temperature detector formed by means of a platinum measuring resistor, a thermistor or a thermocouple, as well as by means of a second coupling body coupling the second temperature detector thermally conductively with the first temperature detector. Said temperature sensor is adapted to register a first measured temperature, namely a temperature at a first temperature measurement location formed by means of the first temperature detector, and to transduce such into a first temperature signal, namely a first electrical measurement signal representing the first measured temperature, for example, with an electrical signal voltage dependent on the first measured temperature and/or an electrical signal current dependent on the first measured temperature, and said temperature sensor is adapted to register a second measured temperature, namely a temperature at a second temperature measurement location formed by means of the second temperature detector, and to transduce such into a second temperature signal, namely a second electrical measurement signal representing the second measured temperature, for example, with an electrical signal voltage dependent on the second measured temperature and/or an electrical signal current dependent on the second measured temperature. The transducer housing and the tube of the transducer apparatus of the invention are additionally adapted to hold a fluid in the intermediate space, for example, a fluid having a specific thermal conductivity of less than 1 W/(m·K), for example, namely air or an inert gas, in order to form a fluid volume surrounding the tube, in such a manner that the outer surface of the wall of the tube facing the intermediate space is contacted by fluid held in the intermediate space, in order to form a second interface of first type. The temperature sensor contacts the outer surface of the wall of the tube to form a first interface of second type, namely an interface between two solid phases, and fluid volume surrounding the tube to form a third interface of first type, and, indeed, in such a manner that a first thermal resistance, R1, opposes a heat flow, Q1, resulting from a temperature difference, ΔT1, reigning between the first interface of second type and the first temperature measurement location, passing totally through the interface, and fowing on to the first temperature measurement location and a second thermal resistance, R2, opposes a heat flow, Q2, resulting from a temperature difference, ΔT2, reigning between the first temperature measurement location and the second temperature measurement location, totally flowing from the first to the second temperature measurement location, respectively a third thermal resistance, R3, opposes a heat flow, Q3, resulting from a temperature difference, ΔT3, reigning between the second temperature measurement location and the third interface of first type, totally flowing from the second temperature measurement location to the interface, equally as well totally passing through the interface.

Moreover, the invention resides also in a measuring system for measuring at least one measured variable, for example, a temperature, a density and/or a viscosity, of a flowing fluid, for example, a gas, a liquid or a flowable dispersion, which measuring system comprises a measuring and operating electronics, for example, one formed by means of a microprocessor, and, for guiding the fluid, an above-referenced transducer apparatus of the invention. In a first embodiment of the transducer apparatus of the invention, it is provided that the first thermal resistance, R1, and the second thermal resistance, R2 fulfill a condition

$0.1 < \frac{R\; 2}{R\; 1} < 200.$

In a second embodiment of the transducer apparatus of the invention, it is provided that the first thermal resistance, R1, the second thermal resistance, R2, and the third thermal resistance, R3, fulfill a condition

$\frac{R\; 3}{{R\; 1} + {R\; 2}} > 1.$

In a third embodiment of the transducer apparatus of the invention, it is provided that the first thermal resistance, R1, and the third thermal resistance, R3, fulfill a condition

$\frac{R\; 3}{R\; 1} > 1.$

In a fourth embodiment of the transducer apparatus of the invention, it is provided that the first thermal resistance, R1, is less than 1000 K/W, and the thermal resistance, R2, is less than 1000 K/W.

In a fifth embodiment of the transducer apparatus of the invention, it is provided that the first thermal resistance, R1, is less than 30 K/W, for example, less than 25 K/W. Developing this embodiment of the invention further, it is, additionally, provided that the first coupling body is composed at least partially, for example, also predominantly or completely, of a material, for example, a thermally conductive adhesive, of which a specific thermal conductivity, λ711, is greater than a specific thermal conductivity, λF, of the fluid in the intermediate space and/or greater than 1 W/(m·K), and of which a specific heat capacity, cp711, is less than a specific heat capacity, cpF, of the fluid in the intermediate space and/or less than 2000 J/(kg·K), for example, in such a manner that a ratio, λ711/λF, of the specific thermal conductivity, λ711, of the material to the specific thermal conductivity, λF, of the fluid in the intermediate space is greater than 2, and/or that a ratio, cp711/cpF, of the specific heat capacity, cp711, of the material to the specific heat capacity, cpF, of the fluid in the intermediate space is less than 0.9. Alternatively or supplementally, the second coupling body can at least partially, for example, also predominantly or completely, comprise a material, for example, a metal, of which material a specific thermal conductivity, λ712, is less than the specific thermal conductivity, λ711, of the material of the first coupling body and/or less than 10 W/(m·K), and/or of which material a specific heat capacity, cp712, is less than the specific heat capacity, cp711, of the material of the first coupling body and/or less than 1000 J/(kg·K).

In a sixth embodiment of the transducer apparatus of the invention, it is provided that the third thermal resistance, R3, has a resistance value greater than 500 K/W, for example, amounting to more than 5000 K/W, and/or less than 20000 K/W, for example, 10000 K/W.

In a seventh embodiment of the transducer apparatus of the invention, it is provided that the temperature sensor contacts by means of the first coupling body the outer surface of the wall of the tube to form the first interface of second type, namely an interface between two solid phases.

In an eighth embodiment of the transducer apparatus of the invention, it is provided that the temperature sensor is formed by means of a third coupling body coupling the second temperature detector thermally with the fluid volume formed in the intermediate space and contacting the fluid volume to form the third interface of first type. Said coupling body can be formed, for example, by means of a synthetic material, e.g. a plastic, applied on the second temperature detector, by means of a textile band or tape applied on the second temperature detector, respectively by means of sheet metal applied on the second temperature detector. Developing this embodiment of the invention further, it is, additionally, provided that the third coupling body is composed at least partially, for example, also predominantly or completely, of a material, of which a specific thermal conductivity, λ713, is greater than a specific thermal conductivity, λF, of the fluid in the intermediate space and/or greater than 1 W/(m·K), and of which a specific heat capacity, cp713, is less than a specific heat capacity, cpF, of the fluid in the intermediate space and/or less than 2000 J/(kg·K), for example, in such a manner that a ratio, λ713/λF, of the specific thermal conductivity, λ713, of the material to the thermal conductivity, λF, of the fluid in the intermediate space is greater than 2, and/or that a ratio, cp713/cpF, of the specific heat capacity, cp713, of the material to the heat capacity, cpF, of the fluid in the intermediate space is less than 0.9.

In a ninth embodiment of the transducer apparatus of the invention, it is provided that the first coupling body has a heat capacity, C1, which is less than 200 J/K, for example, less than 100 J/K, and that the second coupling body has a heat capacity, C2, which is less than 200 J/K, for example, less than 100 J/K, for example, in such a manner that the heat capacity, C1, of the first coupling body and the second heat capacity, C2, of the second coupling body fulfill a condition

$\frac{1}{10} < \frac{C\; 1}{C\; 2} < 1.$

In a 10^(th) embodiment of the transducer apparatus of the invention, it is provided that the wall of the tube has a wall thickness, which amounts to more than 0.5 mm and/or less than 10 mm.

In an 11^(th) embodiment of the transducer apparatus of the invention, it is provided that the tube has an inner diameter, which amounts to more than 0.5 mm and/or less than 200 mm.

In a 12^(th) embodiment of the transducer apparatus of the invention, the tube is so dimensioned that it has an inner diameter to wall thickness ratio, defined as a ratio of an inner diameter of the tube to a wall thickness of the wall of the tube, which amounts to less than 25:1 and/or more than 5:1.

In a 13^(th) embodiment of the transducer apparatus of the invention, it is provided that the first temperature sensor is connected with the outer surface of the wall of the tube, for example, by means of a thermally conductive adhesive, thus, for example, adhesively, to form the first coupling body by the bonding of materials.

In a 14^(th) embodiment of the transducer apparatus of the invention, it is provided that the first coupling body is formed, for example, also exclusively, by means of a synthetic material, such as e.g. an epoxide resin or a silicone, located between the wall of the tube and the first temperature detector, for example, a synthetic material contacting both the outer surface of the wall as well as also the first temperature detector and/or a synthetic material containing metal oxide particles. Developing this embodiment of the invention further, it is, additionally, provided that the synthetic material is, for example, a 1-component or 2-component, silicone rubber, such as e.g. DELO-GUM® 3699, of DELO Industrial Adhesives GmbH & Co KGaA, 86949 Windach, DE.

In a 15^(th) embodiment of the transducer apparatus of the invention, the tube is at least sectionally, for example, predominantly, straight, for example, circularly cylindrically straight.

In a 16^(th) embodiment of the transducer apparatus of the invention, the tube is at least sectionally curved, for example, with a circular arc shape.

In a 17^(th) embodiment of the transducer apparatus of the invention, it is provided that the wall of the tube is at least partially, for example, predominantly or completely, composed of a material, for example, a metal or an alloy, of which a specific thermal conductivity, λ10, is greater than 10 W/(m·K), and of which a specific heat capacity, cp1, is less than 1000 J/(kg·K).

In an 18^(th) embodiment of the transducer apparatus of the invention, it is provided that the wall of the tube is composed of a metal, respectively an alloy, for example steel, titanium, zirconium, tantalum.

In a 19^(th) embodiment of the transducer apparatus of the invention, the tube is adapted to execute mechanical oscillations about an associated static resting position.

In a 20^(th) embodiment of the transducer apparatus of the invention, the tube is further adapted to be flowed through by the fluid and during that to be caused to vibrate, for example, also in such a manner that the tube executes mechanical oscillations about a static resting position associated therewith, mechanical oscillations which are suitable to induce in the flowing fluid Coriolis forces dependent on a mass flow rate, m, and/or that the tube executes mechanical oscillations about a static resting position associated therewith, which are suitable to induce in the fluid frictional forces dependent on a viscosity, η, and/or that the tube executes mechanical oscillations about a static resting position associated therewith, which are suitable to induce in the fluid inertial forces dependent on a density, ρ.

In a further development of the transducer apparatus of the invention, such further comprises an oscillation exciter for exciting and maintaining mechanical oscillations of the at least one tube about an associated static resting position, as well as an oscillation sensor for registering mechanical oscillations of the at least one tube.

In a first embodiment of the measuring system of the invention, the transducer apparatus further comprises an oscillation exciter for exciting and maintaining mechanical oscillations of the at least one tube about an associated static resting position, as well as an oscillation sensor for registering mechanical oscillations of the at least one tube, and the measuring and operating electronics is additionally adapted to generate an exciter signal driving the oscillation exciter for exciting mechanical oscillations of the tube. Developing this embodiment of the invention further, the oscillation exciter is, additionally, adapted by means of the exciter signal to excite, respectively to maintain, mechanical oscillations of the tube. Furthermore, the oscillation sensor is adapted to deliver an oscillatory signal representing oscillations of the at least one tube, and the measuring and operating electronics is adapted, using both the first temperature measurement signal as well as also the second temperature measurement signal as well as the oscillation signal, to generate a density measured value, namely a measured value representing a density of the fluid.

In a second embodiment of the measuring system of the invention, the measuring and operating electronics is adapted, using both the first temperature measurement signal generated by means of the transducer apparatus as well as also the second temperature measurement signal generated by means of the transducer apparatus, to generate a measured value, which represents the at least one measured variable.

In a third embodiment of the measuring system of the invention, the measuring- and operating electronics is adapted, with application both of the first temperature measurement signal generated by means of the transducer apparatus as well as also the second temperature measurement signal generated by means of the transducer apparatus, to generate a measured value, which represents the at least one measured variable.

In a fourth embodiment of the measuring system of the invention, the measuring and operating electronics is adapted, using both the first temperature measurement signal as well as also the second temperature measurement signal, to generate at least one temperature measured value representing a target temperature, namely a temperature at an apparatus reference point predetermined for the measuring system and fixed within the transducer apparatus, for example, an apparatus reference point removed both from the first temperature sensor as well as also from the second temperature sensor and/or located within the tube. Developing this embodiment of the invention further, it is, additionally, provided that the apparatus reference point (poi) is located within the transducer apparatus, for example, namely in the wall of the tube or in the lumen of the tube, for instance, also in such a manner that the temperature measured value represents a tube temperature, namely a temperature assumed by the wall of the tube, respectively in such a manner that the temperature measured value represents a measured fluid temperature, namely a temperature of the fluid guided within the lumen.

A basic idea of the invention is, in conventional measuring systems of the type being discussed, not least by all also in conventional vibronic measuring systems, in the case of ascertaining measured values for a particular target temperature, for example, namely a tube temperature and/or a measured fluid temperature, respectively also in the case of ascertaining measured values for the density and/or the viscosity, to register in a manner accessible for measuring, respectively metrological, processing, an influence of temperature difference existing between the measured fluid temperature, respectively the tube temperature, on the one hand, and the tube ambient temperature, on the other hand, and regularly additionally also fluctuating over a broad temperature range. This is done by using a temperature sensor formed by means of two temperature detectors thermally well, equally as well differently strongly, coupled to the tube of the transducer apparatus and/or differently strongly coupled to the fluid volume surrounding the tube, so that, as a result, the temperature measurement location formed by means of the first of the two temperature detectors assumes a measurement location temperature, which differs from a measurement location temperature of the temperature measurement location formed by means of the second of the two temperature detectors. Knowing the thermal resistances related by the respectively designed construction of the temperature sensor, consequently its earlier very exactly known sizes, respectively ratios, respectively relevant for the heat conduction processes through the temperature sensor, and based on the so forced deviation of the two measurement location temperatures from one another, then the temperature difference existing between the measured fluid temperature and the tube ambient temperature, respectively based thereon, the particular target temperature, for example, namely the tube temperature or also the measured fluid temperature, can be exactly ascertained.

The invention as well as other advantageous embodiments thereof will now be explained in greater detail based on the examples of embodiments shown in the figures of the drawing. Equal parts are provided in all figures with equal reference characters; when perspicuity requires or it otherwise appears sensible, already mentioned reference characters are omitted in subsequent figures. Other advantageous embodiments or further developments, especially also combinations of, first of all, only individually explained aspects of the invention, result, furthermore, from the figures of the drawing, as well as also the dependent claims per se. The figures of the drawing show as follows:

FIG. 1 schematically, an example of an embodiment of a measuring system, especially a measuring system suitable for application in industrial measuring and automation technology, wherein the measuring system comprises: a transducer apparatus having a transducer housing; and a measuring and operating electronics accommodated in an electronics housing—here an electronics housing secured directly on the transducer housing;

FIGS. 2, 3 differently sectioned views of examples of embodiments of a transducer apparatus suitable for a measuring system of FIG. 1 and comprising a tube and two temperature sensors secured thereto and contacting the wall of the tube;

FIG. 4 a resistor network formed by means of a plurality of discrete thermal resistances in the manner of an equivalent circuit, serving for explaining heat fluxes in a transducer apparatus of FIGS. 2, 3, respectively corresponding temperature drops within the transducer apparatus;

FIG. 5 a graph of dependencies of measurement location temperatures (respectively temperature measurement signals derived therefrom) registered in a transducer apparatus of FIGS. 2, 3 by means of its respective temperature sensors for a tube temperature and a tube ambient temperature, respectively a temperature difference existing therebetween; and

FIG. 6 a resistor network formed by means of a plurality of discrete thermal resistances in the manner of an equivalent circuit and serving for explaining heat fluxes, respectively corresponding temperature drops, in a transducer apparatus, including the tube, of FIGS. 2, 3.

FIG. 1 shows schematically a measuring system for measuring at least one measured variable x of a flowing fluid FL1 (measured fluid), such as e.g. a gas, a liquid or a flowable dispersion, having a measured fluid temperature θ_(FL1), which may, in given cases, also be variable as a function of time. The measuring system serves for recurringly ascertaining measured values X_(x) instantaneously representing the measured variable. Measured variable x can be, for example, a density or a viscosity, consequently a measured variable, which has a certain dependence on the respective measured fluid temperature and/or in the case of whose conversion into the respective measured value X_(x) the transducer apparatus causes a temperature dependent measuring error. The measured variable can, however, also be, for example, a temperature (henceforth also referred to as target temperature) of interest at an apparatus reference point (poi) predetermined for the measuring system and located within the transducer apparatus. The measuring system comprises a transducer apparatus MT for producing measurement signals dependent on the at least one measured variable as well as a measuring and operating electronics ME electrically connected with such and supplied with electrical energy especially during operation from the outside via connection cable and/or by means of an internal energy storer, and serving for producing the measured values representing the measured variable(s) registered by means of the transducer apparatus, respectively for sequentially outputting to a corresponding measurement output such measured values as currently valid, measured values of the measuring system.

The measuring and operating electronics ME, formed e.g. by means of at least one microprocessor and/or by means of a digital signal processor (DSP), can, such as indicated in FIG. 1, be accommodated, for example, in a single, in given cases, also chambered, electronics housing 200 of the measuring system. Said electronics housing 200 can, depending on demands on the measuring system, be embodied, for example, also impact- and/or explosion resistantly and/or hermetically sealedly. The measuring device electronics ME includes, as well as also shown schematically in FIG. 1 in the manner of a block diagram, an evaluating circuit μC, which processes measurement signals of the transducer apparatus MT and is formed, for example, by means of a microprocessor. During operation, the evaluating circuit μC generates corresponding measured values for the measured variable to be registered by means of the measuring system. The measured values X_(x) generated by means of the measuring and operating electronics ME can, in the case of the measuring system shown here, be displayed, for example, on-site, namely directly at the measuring point formed by means of the measuring system. For visualizing, on-site, measured values produced by means of the measuring system and/or, in given cases, measuring device internally generated, system status reports, such as, for instance, a report signaling increased measurement accuracy, respectively error, or an alarm signaling a disturbance in the measuring system or at the measuring point formed by means of the measuring system, the measuring system can, as well as also indicated in FIG. 1, have, for example, a display- and servicing element HMI communicating with the measuring and operating electronics, in given cases, also a portable, display- and servicing element HMI, such as, for instance, an LCD—, OLED- or TFT display located in the electronics housing 200 behind a window correspondingly provided therein as well as a corresponding input keypad and/or touch screen. In advantageous manner, the, for example, also (re-)programmable—, respectively remotely parameterable, measuring and operating electronics ME can additionally be so designed that it can, during operation of the measuring system, exchange with an electronic data processing system superordinated thereto, for example, a programmable logic controller (PLC), a personal computer and/or a work station, via a data transmission system, for example, a fieldbus system, such as, for instance, FOUNDATION FIELDBUS, PROFIBUS, and/or wirelessly per radio, measuring—and/or other operating data, such as, for instance, current measured values, system diagnostic values, system status reports or, however, also setting values serving for control of the measuring system.

The measuring- and evaluating circuit μC of the measuring and operating electronics can be implemented, for example, by means of at least one microprocessor and/or microcomputer having a digital signal processor (DSP). The program codes to be executed thereby, as well as also operating parameters serving for control of the respective measuring system, such as e.g. also desired values for control algorithms, implemented by means of the measuring and operating electronics can —, such as also schematically shown in FIG. 1 —, e.g. be stored persistently in a non-volatile data memory EEPROM of the measuring and operating electronics ME and be loaded at startup of the same into a volatile data memory RAM, e.g. one integrated into the microcomputer. Microprocessors suitable for such applications are available from the firm, Texas Instruments Inc., an example being type TMS320VC33.

Furthermore, the measuring and operating electronics ME can be so designed that it can be fed from an external energy supply, for example, also via the aforementioned fieldbus system. For such purpose, the measuring and operating electronics ME can have, for example, an internal energy supply circuit ESC for providing internal supply voltages UN. During operation, the energy supply circuit ESC is fed via the aforementioned fieldbus system by an external energy supply provided in the aforementioned data processing system. In such case, the measuring system can be embodied, for example, as a so-called four conductor device, in the case of which the internal energy supply circuit of the measuring device electronics ME can be connected by means of a first pair of lines with an external energy supply and the internal communication circuit of the measuring and operating electronics ME can be connected by means of a second pair of lines with an external data processing circuit or an external data transmission system. The measuring and operating electronics can, furthermore, however, also be so embodied that it is, such as also shown, among others, in the above mentioned U.S. Pat. No. 7,200,503, U.S. Pat. No. 7,792,646, electrically connectable with the external electronic data processing system by means of a two-conductor connection, configured, for example, as a 4-20 mA electrical current loop, and via that both is supplied with electrical energy as well as also measured values can be transmitted to the data processing system. For the typical case, in which the measuring system is provided for coupling to a fieldbus- or other electronic communication system, the measuring and operating electronics ME, which is, for example, also (re-)programmable on-site and/or via a communication system, can additionally have a corresponding communication interface COM, for example, one conforming to relevant industry standards, such as, for instance, IEC 61158/IEC 61784, for data communication, e.g. for sending measuring- and/or operating data, thus the measured values representing the particular measured variable, to the above mentioned programmable logic controller (PLC) or to a superordinated process control system and/or for receiving settings data for the measuring system. The electrical connecting of the transducer apparatus to the measuring and operating electronics can occur by means of corresponding connecting lines, which run from the electronics housing 200, for example, via an electrical cable feedthrough, into the transducer housing 100 and at least sectionally also within the transducer housing 100. The connecting lines can, in such case, be embodied at least partially as line wires at least sectionally encased by electrical insulation, e.g. in the form of “twisted pair” lines, flat ribbon cables and/or coaxial cables. Alternatively thereto or in supplementation thereof, the connecting lines can be formed at least sectionally also by means of conductive traces of a, for example, flexible, respectively partially rigid and partially flexible, in given cases also lacquered, circuit board; compare for this also the above mentioned US-A 2001/0037690 or WO-A 96/07081.

The transducer apparatus of the measuring system serves—such as schematically shown in FIG. 2, respectively evident from a combination of FIGS. 1 and 2 —, especially to guide during operation a volume portion of the respective fluid FL1 to be measured, respectively serves to be flowed through by the fluid, as well as to provide different measurement signals for physical measured variables respectively to be registered by means of the transducer apparatus, especially namely for measurement location temperatures reigning at different measurement points within the transducer apparatus. The transducer apparatus includes a transducer housing 100 as well as a therein accommodated tube 10 having a lumen 10′ surrounded by a wall, for example, a metal wall, wherein the tube 10 is arranged within a cavity of the transducer housing surrounded by a wall of the transducer housing, for example, a metal wall and/or a wall serving as outer protective shell, in such a manner that between an inner surface 100+ of the wall of the transducer housing 100 facing the cavity and a outer surface 10# of the wall of the tube 10, namely an outer surface of the wall of the tube 10 facing the cavity, an intermediate space 100′ is formed. Tube 10 is, especially, adapted to guide in its lumen the fluid FL1 (respectively, a volume portion thereof) in such a manner that an inner surface 10+ of the wall of the tube facing the lumen is contacted by fluid FL1 guided in the lumen to form a first interface II11 of first type, namely an interface between a fluid and a solid phase, whereby, as a result, a tube temperature θ₁₀, namely a temperature assumed by the wall of the tube 10, is co-determined also by the measured fluid temperature θ_(FL1) of the fluid FL1 instantaneously located in the lumen.

The transducer apparatus can, furthermore, be embodied as a measuring transducer of vibration-type, such as applied, for example, in a vibronic measuring system formed as a Coriolis mass flow measuring device, as a density measuring device and/or as a viscosity measuring device, respectively as a component of such a measuring transducer. Accordingly, the tube is in an additional embodiment of the invention, furthermore, adapted to be flowed through by the fluid FL1 and during that to be caused to vibrate; this, for example, in such a manner that the tube executes mechanical oscillations about a static resting position associated therewith, oscillations which are suitable to induce in the flowing fluid Coriolis forces dependent on a mass flow rate m and/or frictional forces dependent on a viscosity η and/or inertial forces dependent on a density ρ. Particularly for this case, the transducer apparatus is according to an additional embodiment of the invention, furthermore, equipped with an oscillation exciter 41 for exciting and maintaining mechanical oscillations of the at least one tube about an associated static resting position, as well as with at least one oscillation sensor 51 for registering mechanical oscillations of the at least one tube and for generating an oscillation measurement signal s1 representing oscillatory movements of the tube. For this case, in which the transducer apparatus is embodied as a measuring transducer of vibration-type, respectively as a component thereof, there is provided in the measuring and operating electronics ME, furthermore, a corresponding driver circuit Exc, namely one serving for activating the transducer apparatus and, in given cases, also electrically connected with the measuring and evaluating circuit μC, which driver circuit Exc is adapted to provide at least one electrical driver signal e1 for an oscillation exciter provided, in given cases, in the transducer apparatus. Finally, the measuring and operating electronics can for this case also be so embodied that it corresponds as regards circuit construction to one of the measuring and operating electronics known from the above mentioned state of the art, for example, U.S. Pat. No. 6,311,136, or, for example, also to a measurement transmitter of a Coriolis mass flow/density measuring device sold by the applicant, e.g. under the designation “PROMASS 83F”, respectively described at http://www.de.endress.com/#product/83F.

Tube 10 of the transducer apparatus of the invention can be embodied to be at least sectionally straight, consequently sectionally (hollow-)cylindrical, for example, namely circularly cylindrical, and/or at least sectionally curved, for example, namely curved in the form of a circular arc shape. In the example of an embodiment shown here, the—here predominantly, respectively completely, straight—tube, consequently the transducer apparatus formed therewith, is, furthermore, adapted to be inserted into the course of a process line, for example, one formed as a rigid pipeline, guiding the fluid. Especially, the transducer apparatus is, furthermore, adapted to be connected releasably with the process line, for example, a process line in the form of a metal pipeline. For such purpose, there are provided on the inlet side of the transducer apparatus a first connecting flange 13 serving for connecting the tube to a line segment of the process line supplying the fluid FL1 and on the outlet side of the transducer apparatus a second connecting flange 14 serving for connecting the tube to a line segment of the process line draining the fluid. The connecting flanges 13, 14 can, in such case, such as quite usual in the case of transducer apparatuses of the type being discussed, also be integrated terminally in the transducer housing 100, namely be embodied as an integral component of the transducer housing.

In an additional embodiment of the invention, it is, furthermore, provided that the wall of the tube is composed at least partially —, for example, also predominantly or completely—of a material, whose specific thermal conductivity λ10 is greater than 10 W/(m·K) and whose specific heat capacity cp10 is less than 1000 J/(kg·K). As already indicated, the wall can be, for example, of a metal, respectively a metal alloy, for example, namely titanium, zirconium or tantalum, respectively a corresponding alloy thereof, a steel or a nickel based alloy. Furthermore, it is provided that the wall of the tube according to an additional embodiment of the invention has a wall thickness s, which amounts to more than 0.5 mm, and/or an inner diameter, which amounts to more than 0.5 mm. Alternatively or supplementally, the tube is, furthermore, so dimensioned that it has an inner diameter to wall thickness ratio D/s, defined as a ratio of an inner diameter D of the tube to a wall thickness s of the wall of the tube, which amounts to less than 25:1. In an additional embodiment of the invention, it is, furthermore, provided that the wall thickness amounts to less than 10 mm and/or the inner diameter D amounts to less than 200 mm, respectively that the tube is so dimensioned that the inner diameter to wall thickness ratio D/s amounts to more than 5:1. For registering measurement location temperatures reigning within the transducer apparatus and for converting the same into a particular temperature measurement signal, the transducer apparatus of the invention further comprises—such as shown in FIG. 1, respectively 2—, a temperature sensor 70. Temperature sensor 70 is —, as well as also shown schematically in FIG. 2—formed by means of a first temperature detector 701 arranged within the intermediate space 100′ and by means of a second temperature detector 702 likewise arranged within the intermediate space 100′. The two temperature detectors are so positioned that the temperature detector 701 and the temperature detector 702 —, as well as also indicated in FIG. 3—are spaced from one another radially with reference to the longitudinal axis L of the tube, respectively a straight tube segment thereof. The two temperature detectors 701, 702 can, for this purpose—such as evident from a combination of FIGS. 2 and 3 —, for example, also be positioned spaced from one another on one and the same tube radius extending perpendicularly to the longitudinal axis L. For the purpose of providing a thermally conductive connection between the temperature detector 701 and the wall of the tube, the temperature sensor further includes a first coupling body 711 coupling the temperature detector 701 thermally conductively with the wall of the tube. Moreover, the temperature detector 701 and the temperature detector 702 are coupled thermally conductively with one another by means of a second coupling body 712 of the temperature sensor. Furthermore, each of the temperature detectors 701, 702 can be connected with the respectively associated coupling body 711, respectively 712, by means of a suitable material bonding, equally thermally well conductive, connection, for example, by means of an adhesive connection or a solder—, respectively a welded connection, and/or by embedding in the respective coupling body 711, respectively 712.

The temperature sensor of the transducer apparatus of the invention is adapted to transduce a first measurement location temperature θ1, namely a temperature at a first temperature measurement location formed by means of the temperature detector 701, into a first temperature measurement signal θ1, namely a first electrical measurement signal representing the measurement location temperature θ1 as well as to transduce a second measurement location temperature θ2, namely a temperature at a second temperature measurement location formed by means of the temperature detector 702, into a second temperature measurement signal θ2, namely a second electrical measurement signal representing the measurement location temperature θ2. Each of the two temperature detectors 701, 702 can be formed, for example, by means of a platinum measuring resistor, a thermistor or a thermocouple. Accordingly, each of the temperature measurement signals θ1, θ2 can, for example, be so embodied that it has an electrical signal voltage dependent on the respective measurement location temperature and/or an electrical signal current dependent on the measurement location temperature. Moreover, the measuring- and operating electronics ME is according to an additional embodiment of the invention adapted to generate the at least one measured value X_(x) with application both of the first temperature measurement signal θ1 generated by means of the transducer apparatus as well as also at least the second temperature measurement signal θ2 generated by means of the transducer apparatus.

For the purpose of achieving a mechanically fixed and resistant, equally as well thermally well conductive connection between the wall of the tube and the temperature sensor 70, this is according to an additional embodiment of the invention connected with the outer surface 10# of the wall of the tube 10 by the bonding of materials, for example, namely adhesively or by means of a soldered, brazed, respectively welded connection. Serving for manufacturing such a material bonded connection between tube 10 and temperature sensor 70 can be e.g. a thermally conductive adhesive, consequently a synthetic material based on epoxide resin or based on silicone, for example, namely a silicone elastomer or a 1- or 2-component silicone rubber, such as sold by, among others, also the firm, DELO Industrial Adhesives GmbH & Co KGaA, 86949 Windach, DE under the designation DELO-GUM® 3699. The synthetic material applied for connecting temperature sensor 70 and tube 10 can for the purpose of achieving an as good as possible heat conduction additionally also be mixed with metal oxide particles. Furthermore, it is additionally also possible to manufacture the first coupling body 711—partially or completely—of synthetic material, for example, also in such a manner that a plastic molded part placed between temperature detector 701 and wall, respectively contacting both the outer surface 10# of the wall as well as also the temperature detector 701, in given cases, also a monolithic plastic molded part, serves as first coupling body 711, respectively the entire first coupling body 711 is composed of synthetic material —, for example, applied in one or multi layers on the wall of the tube 10, consequently placed between the wall of the tube and the first temperature detector 701. Equally as the coupling body 711, also the second coupling body 712 can be produced of a synthetic material or a metal. Furthermore, the two coupling bodies 711, 712 can by corresponding selection of the materials actually used for their respective manufacture, in each case, be directly so embodied that the specific thermal conductivity λ712 of a material of the second coupling body 712 is less than the specific thermal conductivity λ711 of a material of the first coupling body 711 and/or the specific heat capacity cp712 of the material of the second coupling body 712 is less than the specific heat capacity cp711 of the material of the first coupling body 711. In another embodiment of the invention, also the second coupling body 712 is at least partially produced of a synthetic material, respectively formed by means of a plastic body placed correspondingly between the temperature detector 701 and the temperature detector 702. Moreover, the second coupling body 712 can be connected by material bonding with temperature detector 701, for example, namely also adhesively or by means of a welded—, respectively soldered or brazed connection. In an additional embodiment of the invention, the first coupling body 712 is composed at least partially, for example, also predominantly or completely, of a material, for example, namely a synthetic material or plastic, a ceramic, respectively a metal, of which a specific thermal conductivity λ712 is less than 10 W/(m·K), respectively and/or of which a specific heat capacity cp712 is less 1000 J/(kg·K).

As shown schematically in FIG. 2, respectively FIG. 3, the temperature detector 701 is thermally coupled to the tube, in that the first coupling body 711 contacts the outer surface 10# of the wall of the tube to form a first interface II21 of second type, namely an interface between two solid phases, and the temperature detector 702 is thermally coupled to the tube from farther out, in that the second coupling body 712 contacts the first coupling body 711 to form a second interface II22 of second type. Each of the two interfaces II21, II22 has, in such case, a respective surface area related to, consequently predetermined by, the particular form of construction of the respective coupling body 711, 712. Accordingly, —, as well as also shown simplified in FIG. 4 based on an equivalent circuit for a resistor network formed by means of a plurality of discrete thermal resistances—a first thermal resistance R1 (R1=ΔT1/Q1) thermally conductively connected with the first temperature measurement location—and here principally determined by heat conduction—opposes a heat flux Q1 resulting from a temperature difference ΔT1 reigning between the interface II21 of second type and the first temperature measurement location, equally as well totally passing through the interface II21 and flowing further to the first temperature measurement location, and a second thermal resistance R2 (R2=ΔT2/Q2) thermally conductively connected with the second temperature measurement location—and here likewise principally determined by heat conduction—opposes a heat flux Q2 resulting from a temperature difference ΔT2 reigning between the interface II22 of second type, respectively the first temperature measurement location formed there, and the second temperature measurement location, equally as well totally passing through the interface II22, and flowing further to the second temperature measurement location.

In order to achieve an as good as possible thermal coupling of the temperature detector 701 to the wall of the tube, respectively additionally an as good as possible thermal coupling of the temperature detector 702 to the temperature detector 701, each of the thermal resistances R1 and R2 is, respectively the temperature sensor 70 is, according to an additional embodiment of the invention, so dimensioned that each of the thermal resistances R1 and R2 is less than 1000 K/W. Furthermore, at least the thermal resistance R1, respectively the temperature sensor 70, is also so dimensioned that the thermal resistance R1 is less than 30 K/W, especially less than 25 K/W. In order, moreover, to achieve that the temperature sensor 70 —, as well as also assumed in the case of the (static) calculation model underlying the equivalent circuit diagram shown in FIG. 4—has only a comparatively small, consequently negligible, thermal inertia, respectively each of the two measurement location temperatures can follow, as quickly as possible, changes of the tube temperature θ₁₀, respectively that, conversely, each of the two measurement location temperatures is not or, at most, to only a small degree, dependent on a rate of change of the tube temperature θ₁₀, namely a velocity, with which the tube temperature changes as a function of time, it is, according to an additional embodiment of the invention, furthermore, provided, so to construct each of the coupling body 711 and 712 that both the coupling body 711 as well as also the coupling body 712 have, as a result, in each case, a heat capacity C1, respectively C2, which is less than 2000 J/K; this in advantageous manner, furthermore, such that the heat capacity C1 of the first coupling body 711 and the heat capacity C2 of the second coupling body 712 fulfill a condition 1/1000<C1/C2≦1, and/or that at least the coupling body 711 has a specific heat capacity, which is less than 200 J/(kg·K), as much as possible, however, also less than 100 J/(kg·K). Due to the compact construction typically desired for temperature sensors of the type being discussed as well as the typically used, namely thermally well conductive materials, there is additionally also a close relationship between thermal resistance and heat capacity of the temperature sensor 70, in such a manner that the particular heat capacity—consequently also the above referenced heat capacity C1, respectively C2—is lower, the lower the selection of the particular thermal resistance. Accordingly, through the sizing of the thermal resistances R1, R2 of the coupling bodies 711, respectively 712 in the previously indicated manner, it can, thus, at the same time also be achieved that the temperature sensor 70 has, on the whole, also a comparatively low thermal inertia relative to the tube temperature θ₁₀, respectively each of the two measurement location temperatures can—as desired—quickly follow possible changes of the tube temperature θ₁₀, respectively, conversely, that each of the two measurement location temperatures is not or, at most, only to a small degree, dependent on a rate of change of the tube temperature θ₁₀, namely a velocity, with which the tube temperature θ₁₀ changes as a function of time.

The intermediate space 100′ formed between the inner surface 100+ of the wall of the transducer housing 100 and the outer surface 10# of the wall of the tube 10 is, furthermore,—such as quite usual in the case of transducer apparatuses of the type being discussed and such as indicated in FIG. 2, respectively 3, in each case, schematically by means of the stippling—filled with a fluid FL2 having, for example, a specific thermal conductivity λF of less than 1 W/(m·K) for the purpose of forming a fluid volume surrounding the tube 10. The fluid FL2 in the intermediate space 100′, respectively the fluid volume formed therewith, has a fluid temperature henceforth referred to as the ambient temperature θ_(FL2) of the tube, a fluid temperature, which is, in given cases, also variable as a function of time, and which, at least at times, deviates from the measured fluid temperature θ_(FL1) by more than 1 K (Kelvin), especially, at least at times, by more than 5 K. Accordingly, according to an additional embodiment of the invention, the transducer housing and the tube are adapted to hold the fluid FL2 in the intermediate space 100′, in such a manner that the outer surface 10+ of the wall of the tube facing the intermediate space 100′ is contacted by fluid in the intermediate space FL2 to form a second interface II12 of first type, consequently the tube is thermally coupled to the fluid volume formed in the intermediate space 100′. Serving as fluid FL2 can be, for example, air or an inert gas, such as e.g. nitrogen or a noble gas, for example, helium. As a result of the fact that also an outer surface of the temperature sensor 70 facing the intermediate space 100′ contacts the fluid FL2 to form a third interface II13 of first type (interface between a fluid and a solid phase), the temperature sensor 70 is also thermally coupled to the fluid volume formed in the intermediate space 100′, in such a manner that —, as well as also shown schematically in FIG. 2, respectively 3—a third thermal resistance R3 (R3=ΔT3/Q3) thermally conductively connected with the first temperature measurement location—here namely a third thermal resistance determined by heat conduction, as well as also by heat flux (convection) occurring at the interface II13—opposes a heat flux Q3 resulting from a temperature difference ΔT3 reigning between the interface II13 of first type and the first temperature measurement location, namely a heat flux Q3 flowing from the first temperature measurement location totally to the interface II13, equally as well totally passing through the interface II13. The thermal resistance R3 is in advantageous manner so dimensioned that it is less than 20000 K/W, especially less than 10000 K/W. In order to achieve an in comparison to the thermal coupling to the tube 10 weaker thermal coupling of the temperature sensor 70 to the fluid volume formed in the intermediate space 100′, not least of all also in order to achieve that the therewith registered measurement location temperatures θ1, respectively θ2 are as immune as possible against —, in given cases, also spatially differently—fast time changes of the tube ambient temperature θ_(FL2), respectively that the temperature sensor has relative to the tube ambient temperature θ_(FL2) as much as possible a greater thermal inertia than relative to the tube temperature θ₁₀, the temperature sensor 70 is, according to an additional embodiment of the invention, furthermore, so embodied that the thermal resistance R3 amounts to more than 500 K/W, especially more than 5000 K/W.

In order also to be able to determine the thermal resistance R3 earlier, on the one hand, as simply as possible, on the other hand, however, also to so construct the thermal resistance R3 that its particular examples within a batch, respectively a series, of industrially manufactured transducer apparatuses of the type being discussed have from transducer apparatus to transducer apparatus also an as small as possible scattering, consequently the transducer apparatus is, as a whole, well reproducible, the temperature sensor 70 includes according to an additional embodiment of the invention—and, as well as also shown schematically in FIG. 2, respectively 3, in each case, with a dotted line —, furthermore, a third coupling body 713 coupling its temperature detector 702 thermally with the fluid volume formed in the intermediate space and contacting the fluid volume to form the third interface II13 of first type. Coupling body 713 is composed in accordance with other embodiments of the invention at least partially, especially namely predominantly or completely, of a material, of which a specific thermal conductivity λ723 is greater than the specific thermal conductivity λF of the fluid in the intermediate space FL2 and/or greater than 0.1 W/(m·K), and of which a specific heat capacity cp723 is less than a specific heat capacity cpF of the fluid in the intermediate space FL2 and/or less than 2000 J/(kg·K). In advantageous manner, the material of the coupling body 713 is so selected, matched to the fluid in the intermediate space FL2, that a ratio λ723/λF of the specific thermal conductivity λ723 of the material to the thermal conductivity λF of the fluid in the intermediate space FL2 is greater than 0.2, and/or that a ratio cp723/cpF of the specific heat capacity cp723 of the material to the heat capacity cpF of the fluid in the intermediate space FL2 is less than 1.5. Coupling body 713 can be formed —, for example, also completely—by means of a synthetic material, such as e.g. an epoxide resin or a silicone, for example, one also mixed with metal oxide particles, applied on the second temperature detector 702 of the temperature sensor 70. Alternatively or supplementally, the coupling body 713 can be formed, in given cases, also completely, by means of a textile band or tape applied to the temperature detector 702, for example, a glass fiber textile band or tape, respectively also by means of sheet metal applied to the temperature detector 702, such as e.g. a sheet metal strip of stainless steel.

In order, on the one hand, to provide the temperature sensor 70 with an as small as possible thermal inertia relative to changes of the tube temperature as a function of time, while, on the other hand, also achieving an as good as possible thermal coupling of the temperature sensor 70 to the wall of the tube also with an as compact as possible construction, the first coupling body 711 according to an additional embodiment of the invention is at least partially —, for example, also predominantly or completely—made of a material, for example, namely a thermally conductive adhesive, of which material a specific thermal conductivity λ711 is greater than a specific thermal conductivity λF of the fluid in the intermediate space FL2 and/or greater than 1 W/(m·K). In advantageous manner, the material of the coupling body 711 is, in such case, furthermore, so selected that a ratio λ711/λF of the specific thermal conductivity λ711 of the material of the coupling body 711 to the specific thermal conductivity λF of the fluid in the intermediate space FL2 is greater than 2, and/or that a ratio cp711/cpF of a specific heat capacity cp711 of the material of the coupling body 711 to the heat capacity cpF of the fluid in the intermediate space FL2 is less than 1.5, especially in such a manner that the specific heat capacity cp711 is less than a specific heat capacity cpF of the fluid in the intermediate space.

Due to the thermal coupling of the temperature sensor 70 to the wall of the tube, on the one hand, respectively to the fluid volume surrounding such, on the other hand, —with or without coupling body 713—each of the measurement location temperatures θ1, θ2, is, on the one hand, determined by a temperature difference ΔT′ (ΔT′=θ₁₀−θ_(FL2)) existing between the tube temperature θ₁₀ and the tube ambient temperature θ_(FL2), respectively by a temperature difference ΔT″ (ΔT″=θ_(FL1)−θ_(FL2)) existing between the measured fluid temperature θ_(FL1) and the tube ambient temperature θ_(FL2), and, on the other hand, however, also, in each case, by the actual values of the above-mentioned thermal resistances R1, R2, and R3, respectively resistance ratios resulting therefrom. Under the assumption made for the calculation model underlying the equivalent circuit diagram illustrated in FIG. 4 that heat flux Q2 traversing the thermal resistance R2 corresponds to the heat flux Q1 traversing the thermal resistance R1 and further the traversing heat flux Q3 traversing the thermal resistance R3 corresponds to the heat flux Q2 traversing the thermal resistance R2, consequently Q3=Q2=Q1, it can, first of all, be derived that the measurement location temperature θ1, respectively the measurement location temperature θ2, fulfill approximately, respectively in the case of essentially stationary temperature distribution within the transducer apparatus, among other things, one of the conditions:

$\begin{matrix} {{\vartheta 1} = {{\left( {\vartheta_{{FL}\; 2} - \vartheta_{10}} \right) \cdot \frac{R\; 1}{{R\; 1} + {R\; 3}}} + {{\left. \vartheta_{10} \right.\sim{- \left( {\vartheta_{{FL}\; 1} - \vartheta_{{FL}\; 2}} \right)}} \cdot \frac{R\; 1}{{R\; 1} + {R\; 3}}} + \vartheta_{10}}} & (1) \\ {{\vartheta 2} = {{\left( {\vartheta_{{FL}\; 2} - \vartheta_{10}} \right) \cdot \frac{{R\; 1} + {R\; 2}}{{R\; 1} + {R\; 3}}} + {{\left. \vartheta_{10} \right.\sim{- \left( {\vartheta_{{FL}\; 1} - \vartheta_{{FL}\; 2}} \right)}} \cdot \frac{{R\; 1} + {R\; 2}}{{R\; 1} + {R\; 3}}} + \vartheta_{10}}} & (2) \\ {{\vartheta 1} = {{\left( {\vartheta_{10} - \vartheta_{{FL}\; 2}} \right) \cdot \frac{R\; 3}{{R\; 1} + {R\; 3}}} + {{\left. \vartheta_{{FL}\; 2} \right.\sim{- \left( {\vartheta_{{FL}\; 1} - \vartheta_{{FL}\; 2}} \right)}} \cdot \frac{R\; 3}{{R\; 1} + {R\; 3}}} + \vartheta_{{FL}\; 2}}} & (3) \\ {{\vartheta 2} = {{\left( {\vartheta_{10} - \vartheta_{{FL}\; 2}} \right) \cdot \frac{{R\; 3} - {R\; 2}}{{R\; 1} + {R\; 3}}} + {{\left. \vartheta_{{FL}\; 2} \right.\sim{- \left( {\vartheta_{{FL}\; 1} - \vartheta_{{FL}\; 2}} \right)}} \cdot \frac{{R\; 3} - {R\; 2}}{{R\; 1} + {R\; 3}}} + \vartheta_{{FL}\; 2}}} & (4) \end{matrix}$

respectively that the measurement location temperatures θ1, θ2 depend according to these conditions on the tube ambient temperature θ_(FL2) as well as the measured fluid temperature θ_(FL1), respectively the tube temperature θ₁₀. Furthermore, there results, additionally, that also a measurement location temperature difference ΔT12=θ1−θ2 corresponding to a difference of the two measurement location temperatures θ1, θ2 represented by the temperature measurement signals θ1, θ2 is at least approximately proportional to the previously indicated temperature difference ΔT′ between the tube temperature θ₁₀ and the tube ambient temperature θ_(FL2) according to the relationship illustrated graphically in FIG. 5:

$\begin{matrix} {{{\vartheta 1} - {\vartheta 2}} = {\left( {\vartheta_{10} - \vartheta_{{FL}\; 2}} \right) \cdot \left( {- \frac{R\; 2}{{R\; 1} + {R\; 3}}} \right)}} & (5) \end{matrix}$

respectively that, conversely, the tube temperature θ₁₀ is determinable from the two measurement location temperatures θ1, θ2 according to the relationship:

$\begin{matrix} {\vartheta_{10} = {{\left( {1 + \frac{R\; 1}{R\; 2}} \right) \cdot {\vartheta 1}} - {\frac{R\; 1}{R\; 2} \cdot {\vartheta 2}}}} & (6) \end{matrix}$

Knowing the thermal resistances R1, R2, R3, respectively the thermal resistance ratio R1/R2, thus, e.g. the temperature difference ΔT′, respectively also the tube temperature θ₁₀, can be directly calculated based on the two measurement location temperatures θ1, θ2, respectively their measurement location temperature difference ΔT12.

Each of the previously indicated thermal resistances R1, R2, and R3 is—such as already mentioned —, in each case, decisively, respectively completely, defined by material properties, such as e.g. a specific thermal conductivity λ, as well as dimensions of the respective coupling body, respectively the wall of the tube, such as e.g. a particular length L_(th) of the respective coupling body effective for the respectively traversing heat flux as well as a surface area A_(th) of a particular cross sectional area of the respective coupling body effective for the heat flux, for example, thus the surface area of the interface II21, and/or by corresponding material properties of the wall of the tube 10, respectively of the fluid FL2 in the intermediate space 100′, consequently already alone by parameters earlier at least approximately known, equally as well essentially unchangeable over a longer operational time frame. Thus, each of the thermal resistances R1, R2, R3, can be sufficiently exactly determined earlier by means of such parameters (λ, A_(th), L_(th)), for example, by experimental measurements and/or calculations. For example, based on the known relationship:

$\begin{matrix} {{Rth} = {\frac{\Delta \; T}{Q} = \frac{L_{eff}}{\lambda \cdot A_{eff}}}} & (7) \end{matrix}$

a heat conduction resistance co-determining the thermal resistance R1, respectively R2—namely a heat conduction resistance representing a temperature drop related to a heat flux due to heat conduction processes—can be quantified, for example, namely calculated in units of K/W (Kelvin per Watt). Knowing the material properties of the materials respectively actually used for manufacture of the temperature sensors as well as the actual shape and dimensions of the above-mentioned interfaces II13, II21 formed by means of the temperature sensor, also the resistance values for the above indicated, heat transfer resistances respectively co-determining the thermal resistances R1, R2, R3 can be sufficiently exactly established, respectively sufficiently exactly earlier ascertained. Alternatively or in supplementation, the thermal resistances R1, R2, R3, respectively the corresponding thermal resistance ratio R1/R2, can, for example, also be ascertained experimentally by means of calibration measurements performed on the respective transducer apparatus.

Further taking into consideration an additional thermal resistance represented by the wall of the tube 10 and causing a temperature difference ΔT10 between the interface II11 (first interface of first type) and the interface II12 (second interface of first type), namely —, as well as also illustrated in FIG. 6 based on an equivalent circuit diagram correspondingly supplemented in comparison to that in FIG. 4—a fourth thermal resistance R4 opposing the heat flux Q1 also flowing within the wall of the tube between the interface II11 of first type and the interface II12 of first type, additionally also a dependence of the measurement location temperature difference ΔT12 on the temperature difference ΔT″ (ΔT″=θ_(FL1)−θ_(FL2)) existing between the measured fluid temperature θ_(FL1) and the tube ambient temperature θ_(FL2), respectively, conversely, also a dependence of the measurement location temperature difference ΔT12 on the temperature difference ΔT″ (ΔT″=θ_(FL1)−θ_(FL2)) existing between the measured fluid temperature θFL1 and the tube ambient temperature θ_(FL2), can be formulated, respectively, in each case, expressed in the form of a corresponding formula:

$\begin{matrix} {{{{\vartheta 1} - {\vartheta 2}} = {\left( {\vartheta_{{FL}\; 1} - \vartheta_{{FL}\; 2}} \right) \cdot \left( {- \frac{R\; 2}{{R\; 1} + {R\; 3} + {R\; 4}}} \right)}},{respectively}} & (8) \\ {\vartheta_{10} = {{\left( {1 + \frac{{R\; 1} + {R\; 4}}{R\; 2}} \right) \cdot {\vartheta 1}} - {\frac{{R\; 1} + {R\; 4}}{R\; 2} \cdot {{\vartheta 2}.}}}} & (9) \end{matrix}$

Also, this heat conduction resistance R4 represented by the wall of the tube can be basically earlier sufficiently exactly quantified, namely calculated based on material properties of the tube, such as, for instance, its specific thermal conductivity λ10, respectively specific heat capacitance cp10, as well as its dimensions, especially its wall thickness s, for example, according to one of the formulas based on variation of the previously indicated relationship (7) corresponding to the equivalent circuit diagram shown in FIG. 6:

$\begin{matrix} {{R\; 4} = {\frac{\Delta \; T\; 10}{Q\; 1} \approx {\frac{L_{eff}}{{\lambda 10} \cdot A_{eff}}.}}} & (10) \end{matrix}$

Investigations have, in such case, furthermore, shown that, in the case of using the wall thickness s as effective length L_(eff) (s→L_(eff)), a resistance value then based on twice the area of the associated interface II21, consequently ascertained based on twice the area A_(th) (2·A_(th) A_(eff)) of the cross sectional area of the associated coupling body 711 effective for the heat flux Q1 is a very exact estimation for the heat conduction fraction of the thermal resistance R4 effective for the heat flux Q1, consequently is, as a whole, a good approximation for the respective thermal resistance R4.

Since basically each of the above indicated thermal resistances R1, R2, R3, R4, respectively each of the resistance ratios derived therefrom, is earlier determinable, namely quantifiable, based on the measurement location temperatures θ1, θ2 registered by means of the temperature sensor 70, respectively the temperature measurement signals θ1, θ2 respectively representing these, accordingly also the tube temperature θ₁₀—, for example, namely in application of Equation (6)—and/or the measured fluid temperature θ_(FL1)—, for example, namely in application of Equation 9—can be calculated, respectively measured.

The measuring- and operating electronics ME is, consequently, according to an additional embodiment of the invention, furthermore, also adapted, with application both of the first temperature measurement signal θ1 as well as also the second temperature measurement signal θ2, to generate at least one target temperature measured value X_(θ), namely a measured value representing the particular target temperature, for example, namely the tube temperature or the measured fluid temperature; this, for example, in such a manner that the measuring- and operating electronics ME, first of all, ascertains, based on the temperature measurement signal θ1, a first measurement location temperature measured value X₁ representing the measurement location temperature θ1 and, based on the temperature measurement signal θ2, a second measurement location temperature measured value X₂ representing the measurement location temperature θ2, and thereafter calculates the target temperature measured value X_(θ) with application both of the measurement location temperature measured value X₁ as also the measurement location temperature measured value X₂. The calculating of the target temperature measured value X_(θ) can occur e.g. in such a manner that the target temperature measured value is ascertained according to a formula dependent on the measurement location temperature measured values X₁, X₂ as well as on earlier ascertained numerical constants α, β, stored in the measuring- and operating electronics ME, respectively according to a formula:

X _(θ) =α·X _(θi) +β·X _(θ2)  (11)

and consequently representing a temperature at a apparatus reference point (poi) established by the size of the constants α, β, respectively a size ratio α/β derived therefrom. In the case of application of only two measurement location temperature measured values ascertained based on the temperature measurement signals, the constants α, β contained in the above formula are so selected in advantageous manner that they fulfill the condition α+β=1. The constants α, β can, in such case, be so defined that the apparatus reference point ultimately set thereby is located removed both from the first temperature sensor 71 as well as also from the second temperature sensor 72, especially it is located within the tube; this, for example, also such that the target temperature represented by the target temperature measured value corresponds to the measured fluid temperature θ_(FL1) or also the tube temperature θ₁₀. The tube temperature θ₁₀ is, not least of all for the above-described case, in which the transducer apparatus MT is embodied as a measuring transducer of vibration-type, of special interest, since, among other things, a modulus of elasticity of the respective material of the wall of the tube, as well as also spatial dimensions of the tube, consequently the thereby defined oscillation characteristics of the respective tube, are mentionably also dependent on the tube temperature θ₁₀. For example, —namely in application of Eq. (6)—the apparatus reference point can be positioned at the interface II21 of second type, consequently (virtually), respectively in, the wall of the tube 10, respectively the measuring- and operating electronics ME can be correspondingly adapted to ascertain, respectively to output, the target temperature measured value X_(θ) as measured value for the tube temperature θ₁₀, in that the constants α, β are so selected that thereby the condition

$\begin{matrix} {\alpha = {1 + \frac{R\; 1}{R\; 2}}} & (12) \end{matrix}$

as well as the condition:

$\begin{matrix} {\beta = {- \frac{R\; 1}{R\; 2}}} & (13) \end{matrix}$

and/or the condition:

β=1−α  (14)

are fulfilled. Alternatively or supplementally, —namely with application of Eq. (9)—the apparatus reference point can, however, also be positioned at the interface II11 of first type, consequently (virtually) within the lumen 10′ of the tube 10, respectively in the fluid FL1 guided therein, respectively the measuring- and operating electronics ME can correspondingly be adapted to ascertain, respectively to output, the target temperature measured value X_(θ) as measured value for the measured fluid temperature θ_(FL1). This can be implemented taking into consideration also the thermal resistance R4 provided by the wall of the tube in simple manner by so selecting the constants α, β that the condition:

$\begin{matrix} {\alpha = {1 + \frac{{R\; 1} + {R\; 4}}{R\; 2}}} & (15) \end{matrix}$

as well as the condition:

$\begin{matrix} {\beta = {- \frac{{R\; 1} + {R\; 4}}{R\; 2}}} & (16) \end{matrix}$

are fulfilled.

From the combination of the equivalent circuit diagram illustrated in FIG. 4 and Equation (5), respectively (6), there results, furthermore, that—in order to be able to actually explain the tube temperature θ₁₀ as a function of temperature differences ΔT1, ΔT2, respectively the measurement location temperatures θ1, θ2—the thermal resistances R1 and R2 resulting therefrom are basically to be so sized that the temperature differences ΔT1, ΔT2, respectively measurement location temperatures θ1, θ2, differ from one another, consequently the measurement location temperature difference ΔT12 derived therefrom, as a result, is mentionably different from zero, respectively the following relationships hold, respectively must hold, for the temperature differences ΔT1, ΔT2:

$\frac{\Delta \; T\; 1}{\Delta \; T\; 2} = {\frac{{\vartheta 1} - \vartheta_{10}}{{\vartheta 2} - \vartheta_{10}} = {{\frac{R\; 1}{{R\; 1} + {R\; 3}} \cdot \frac{{R\; 1} + {R\; 3}}{{R\; 1} + {R\; 2}}} = {\frac{1}{1 + \frac{R\; 2}{R\; 1}}\overset{!}{\neq}1.}}}$

Taking this into consideration and with application of the above Equations (1) and (2), the thermal resistances R1, R2, R3, R4 according to an additional embodiment of the invention are, consequently, furthermore, so dimensioned that they fulfill a condition:

$\begin{matrix} {\frac{R\; 2}{R\; 1} > 0} & (17) \end{matrix}$

In order, in such case, also to be able to cancel possible measuring inaccuracies of the temperature detectors of the temperature sensor, respectively measurement uncertainties, respectively confidence intervals, caused by manufacturing tolerances, for instance, in such a manner that a temperature difference ΔT′ having a positive sign is always represented by an equally positive instantaneous measurement location temperature difference ΔT12, the above discussed thermal resistances R1, R2 are according to an additional embodiment of the invention, furthermore, so sized, that, as a result, also the condition:

$\begin{matrix} {\frac{R\; 2}{R\; 1} > {0,1}} & (18) \end{matrix}$

is fulfilled. In order, furthermore, also to achieve that an influence of the tube temperature is also sufficient in the case of the measurement location temperature θ2, respectively that the measurement location temperature θ2 is dependent in like measure on the tube temperature as in the case of the measurement location temperature θ1, the thermal resistances R1, R2 are, in advantageous manner, furthermore, so sized that they also fulfill a condition:

$\begin{matrix} {{\frac{R\; 2}{R\; 1} < 200},} & (19) \end{matrix}$

especially namely also a condition:

$\begin{matrix} {\frac{R\; 2}{R\; 1} < 100} & (20) \end{matrix}$

In order, conversely, also to be able to assure that an influence of the tube ambient temperature both on the measurement location temperature θ1 as well as also the measurement location temperature θ2 is as small as possible, respectively that the measurement location temperature θ2 is in similarly small measure dependent on the tube ambient temperature as in the case of the measurement location temperature θ1, the thermal resistances R1, R2 are, furthermore, according to an additional embodiment of the invention so sized that they also fulfill a condition:

$\begin{matrix} {1 < \frac{R\; 3}{{R\; 1} + {R\; 2}}} & (21) \end{matrix}$

especially namely also a condition:

$\begin{matrix} {1 < \frac{R\; 3}{R\; 1}} & (22) \end{matrix}$ 

1-30. (canceled)
 31. A transducer apparatus, comprising: a transducer housing having a cavity encased by a wall, especially a metal wall; a tube having a lumen surrounded by a wall, especially a metal wall, said tube is arranged within said cavity of said transducer housing in such a manner that between an inner surface of the wall of said transducer housing facing said cavity and an outer surface of the wall of said tube facing said cavity an intermediate space is formed, and said tube is adapted to guide in its lumen a fluid, especially a fluid flowing at least at times, especially a gas, a liquid or a flowable dispersion, in such a manner that said inner surface of the wall of said tube facing the lumen is contacted by fluid guided in the lumen in order to form a first interface of a first type, namely an interface between a fluid and a solid phase; a temperature sensor formed by means of a first temperature detector arranged within said intermediate space, especially said first temperature detector formed by means of a platinum measuring resistor, a thermistor or a thermocouple; a first coupling body coupling said first temperature detector thermally conductively with the wall of said tube; a second temperature detector spaced from said first temperature detector and arranged within said intermediate space, especially a second temperature detector formed by means of a platinum measuring resistor, a thermistor or a thermocouple; a second coupling body coupling said second temperature detector thermally conductively with said first temperature detector; a first thermal resistance, R1; a second thermal resistance, R2; and a third thermal resistance, R3, wherein: said temperature sensor is adapted to register a first measured temperature, namely a temperature at a first temperature measurement location formed by means of said first temperature detector, and to transduce such into a first temperature signal, namely a first electrical measurement signal representing the first measured temperature, especially a first electrical measurement signal having an electrical signal voltage dependent on said first measured temperature and/or an electrical signal current dependent on said first measured temperature; said temperature sensor is adapted to register a second measured temperature, namely a temperature at a second temperature measurement location formed by means of said second temperature detector, and to transduce such into a second temperature signal, namely a second electrical measurement signal representing the second measured temperature, especially a second electrical measurement signal having an electrical signal voltage dependent on said second measured temperature and/or an electrical signal current dependent on said second measured temperature; said transducer housing and said tube are adapted to hold a fluid in said intermediate space, especially a fluid having a specific thermal conductivity of less than 1 W/(m·K), especially air or an inert gas, in order to form a fluid volume surrounding said tube, in such a manner that said outer surface of the wall of said tube facing said intermediate space is contacted by fluid held in said intermediate space, in order to form a second interface of a first type; said temperature sensor contacts said outer surface of the wall of said tube to form a first interface of second type, namely an interface between two solid phases; said temperature sensor contacts the fluid volume surrounding said tube to form a third interface of a first type, in such a manner that; said first thermal resistance, R1, opposes a heat flux, resulting from a temperature difference, reigning between said first interface of a second type and said first temperature measurement location, totally passing through the interface, and flowing further to said first temperature measurement location; said second thermal resistance, R2, opposes a heat flux, resulting from a temperature difference, reigning between said first temperature measurement location and said second temperature measurement location, and flowing totally from the first temperature measurement location to the second temperature measurement location; and said third thermal resistance, R3, opposes a heat flux, resulting from a temperature difference, reigning between said second temperature measurement location and said third interface of a first type, flowing totally from said second temperature measurement location to said interface, and equally as well passing totally through the interface.
 32. The transducer apparatus as claimed in claim 31, wherein: said first thermal resistance, R1, and said second thermal resistance, R2 fulfill a condition $0.1 < \frac{R\; 2}{R\; 1} < 200.$
 33. The transducer apparatus as claimed in claim 31, wherein: said first thermal resistance, R1, said second thermal resistance, R2, and said third thermal resistance, R3 fulfill a condition $\frac{R\; 3}{{R\; 1} + {R\; 2}} > 1.$
 34. The transducer apparatus as claimed in claim 31, wherein: said first thermal resistance, R1, and said third thermal resistance, R3 fulfill a condition $\frac{R\; 3}{R\; 1} > 1.$
 35. The transducer apparatus as claimed in claim 31, wherein: said first thermal resistance, R1, is less than 1000 K/W, and said thermal resistance, R2, is less than 1000 K/W.
 36. The transducer apparatus as claimed in claim 31, wherein: said first thermal resistance, R1, is less than 30 K/W, especially less than 25 K/W.
 37. The transducer apparatus as claimed in claim 31, wherein: said first coupling body is composed at least partially, especially predominantly or completely, of a material, especially a thermally conductive adhesive, of which a specific thermal conductivity, λ711, is greater than a specific thermal conductivity, λF, of the fluid in the intermediate space and/or greater than 1 W/(m·K), and of which a specific heat capacity, cp711, is less than a specific heat capacity, cpF, of the fluid in the intermediate space and/or less than 2000 J/(kg·K), especially in such a manner that a ratio, λ711/λF, of the specific thermal conductivity, λ711, of the material to the specific thermal conductivity, λF, of the fluid in the intermediate space is greater than 2, and/or that a ratio, cp711/cpF, of the specific heat capacity, cp711, of the material to the specific heat capacity, cpF, of the fluid in the intermediate space is less than 0.9.
 38. The transducer apparatus as claimed in claim 27, wherein: said second coupling body is composed at least partially, especially predominantly or completely, of a material, especially a synthetic material, a ceramic, respectively a metal, of which material a specific thermal conductivity, λ712, is less than the specific thermal conductivity, λ711, of the material of the first coupling body and/or less than 10 W/(m·K), and/or of which material a specific heat capacity, cp712, is less than the specific heat capacity, cp711, of the material of said first coupling body and/or less 1000 J/(kg·K).
 39. The transducer apparatus as claimed in claim 31, wherein: said third thermal resistance, R3, has a resistance value amounting to more than 500 K/W, especially more than 5000 K/W, and/or less than 20000 K/W, especially 10000 K/W.
 40. The transducer apparatus as claimed in claim 31, wherein: said temperature sensor contacts by means of said first coupling body the outer surface of the wall of the tube to form said first interface of a second type, namely an interface between two solid phases.
 41. The transducer apparatus as claimed in claim 31, wherein: said temperature sensor is formed by means of a third coupling body coupling said second temperature detector thermally with the fluid volume formed in the intermediate space and contacting the fluid volume to form said third interface of a first type.
 42. The transducer apparatus as claimed in claim 41, wherein: said third coupling body is formed, especially exclusively, by means of a synthetic material, especially an epoxide resin or a silicone, applied on said second temperature detector, especially a synthetic material mixed with metal oxide particles.
 43. The transducer apparatus as claimed in claim 41, wherein: said third coupling body is formed, especially exclusively, by means of a textile band or tape applied on said second temperature detector, especially a glass fiber textile band or tape.
 44. The transducer apparatus as claimed in claim 41, wherein: said third coupling body is formed, especially exclusively, by means of sheet metal, especially a sheet metal strip of stainless steel, applied on said second temperature detector.
 45. The transducer apparatus as claimed in claim 41, wherein: said third coupling body is composed at least partially, especially predominantly or completely, of a material, of which a specific thermal conductivity, λ713, is greater than a specific thermal conductivity, λF, of the fluid in the intermediate space and/or greater than 1 W/(m·K), and of which a specific heat capacity, cp713, is less than a specific heat capacity, cpF, of the fluid in the intermediate space and/or less than 2000 J/(kg·K), especially in such a manner that a ratio, λ713/λF, of the specific thermal conductivity, λ713, of the material to the thermal conductivity, λF, of the fluid in the intermediate space is greater than 2, and/or that a ratio, cp713/cpF, of the specific heat capacity, cp713, of the material to the heat capacity, cpF, of the fluid in the intermediate space is less than 0.9.
 46. The transducer apparatus as claimed in claim 31, wherein: said first coupling body has a heat capacity, C1, which is less than 200 J/K, especially less than 100 J/K; and said second coupling body has a heat capacity, C2, which is less than 200 J/K, especially less than 100 J/K, especially in such a manner that the heat capacity, C1, of said first coupling body and the second heat capacity, C2, of said second coupling body fulfill a condition $\frac{1}{10} < \frac{C\; 1}{C\; 2} < 1.$
 47. The transducer apparatus as claimed in claim 46, wherein: the heat capacity, C1, of said first coupling body and the second heat capacity, C2, of said second coupling body fulfill a condition, ${\frac{1}{10} < \frac{C\; 1}{C\; 2} < 1},$ especially a condition, $0.2 < \frac{C\; 1}{C\; 2} < {0.9.}$
 48. The transducer apparatus as claimed in claim 31, wherein: the wall of said tube has a wall thickness, s, which is greater than 0.5 mm and/or less than 10 mm; and/or said tube has an inner diameter, D, which is greater than 0.5 mm and/or less than 200 mm; and/or said tube is so sized that it has an inner diameter to wall thickness ratio, D/s, defined as a ratio of an inner diameter, D, of the tube to a wall thickness, s, of the wall of the tube, which is less than 25:1 and/or greater than 5:1.
 49. The transducer apparatus as claimed in claim 31, wherein: said temperature sensor is connected with the outer surface of the wall of said tube, especially by means of a thermally conductive adhesive, thus especially adhesively, to form said first coupling body by the bonding of materials.
 50. The transducer apparatus as claimed in claim 31, wherein: said first coupling body is formed, especially exclusively, by means of a synthetic material, especially an epoxide resin or a silicone, located between the wall of said tube and said first temperature detector, especially a synthetic material both contacting the outer surface of the wall as well as also said first temperature detector and/or containing metal oxide particles.
 51. The transducer apparatus as claimed in claim 50, wherein: the synthetic material is a silicone rubber, especially 1-component or 2-component, silicone rubber, especially DELO-GUM® 3699 of DELO Industrial Adhesives GmbH & Co KGaA, 86949 Windach, Germany.
 52. The transducer apparatus as claimed in claim 31, wherein” said tube is at least sectionally, especially predominantly, straight, especially circularly cylindrically straight; and/or wherein said tube is at least sectionally curved, especially with a circular arc shape; and/or the wall of said tube is composed at least partially, especially predominantly or completely, of a material, especially a metal or an alloy, of which a specific thermal conductivity, λ10, is greater than 10 W/(m·K), and of which a specific heat capacity, cp1, is less than 1000 J/(kg·K); and/or the wall of said tube is composed of a metal, respectively an alloy, especially of steel, titanium, zirconium, tantalum; and/or said tube is adapted to execute mechanical oscillations about an associated static resting position.
 53. The transducer apparatus as claimed in claim 31, wherein: said tube is further adapted to be flowed through by the fluid and during that to be caused to vibrate, especially in such a manner that said tube executes mechanical oscillations about a static resting position associated therewith, oscillations which are suitable to induce in the flowing fluid Coriolis forces dependent on a mass flow rate, m; and/or that said tube executes mechanical oscillations about a static resting position associated therewith, oscillations which are suitable to induce in the fluid frictional forces dependent on a viscosity, η; and/or that said tube executes mechanical oscillations about a static resting position associated therewith, oscillations which are suitable to induce in the fluid inertial forces dependent on a density, ρ.
 54. The transducer apparatus as claimed in claim 31, further comprising: an oscillation exciter for exciting and maintaining mechanical oscillations of the at least one tube about an associated static resting position; as well as an oscillation sensor for registering mechanical oscillations of the at least one tube.
 55. A measuring system for measuring at least one measured variable, especially a temperature, a density and/or a viscosity, of a flowing fluid, especially a gas, a liquid or a flowable dispersion, which measuring system comprises: for guiding the fluid, a transducer apparatus as claimed in claim 31; and a measuring and operating electronics, especially one formed by means of a microprocessor.
 56. The measuring system as claimed in claim 55, having a transducer apparatus as claimed in claim 54, wherein: the measuring and operating electronics is adapted to generate an exciter signal driving said oscillation exciter for exciting mechanical oscillations of said tube; and said oscillation exciter is adapted by means of the exciter signal to excite, respectively to maintain, mechanical oscillations of said tube.
 57. The measuring system as claimed in claim 56, wherein: said oscillation sensor is adapted to deliver an oscillatory signal representing oscillations of said at least one tube; and said measuring and operating electronics is adapted, using both the first temperature measurement signal as well as also the second temperature measurement signal, as well as the oscillation signal, to generate a density measured value, namely a measured value representing a density, p, of the fluid.
 58. The measuring system as claimed in claim 55, wherein: said measuring and operating electronics is adapted, using both the first temperature signal generated by means of the transducer apparatus as well as also the second temperature signal generated by means of the transducer apparatus, to generate a measured value, which represents the at least one measured variable.
 59. The measuring system as claimed in claim 55, wherein: said measuring and operating electronics is adapted, using both the first temperature measurement signal as well as also the second temperature measurement signal, to generate at least one temperature measured value representing a target temperature, namely a temperature at an apparatus reference point predetermined for the measuring system and fixed within the transducer apparatus, especially an apparatus reference point removed both from said first temperature sensor as well as also from said second temperature sensor and/or located within said tube.
 60. The measuring system as claimed in claim 59, wherein: the apparatus reference point is located within the transducer apparatus, especially in the wall of said tube or in the lumen of said tube, especially in such a manner that the temperature measured value represents a tube temperature, namely a temperature assumed by the wall of said tube, respectively in such a manner that the temperature measured value represents a measured fluid temperature, namely a temperature of the fluid guided within the lumen. 